I don't even almost have a set answer to this question. It completely depends on the person, the energy flow, other circumstances in my life...
For my husband and I, we met a couple times casually because we had the same social circle, but we were never really friends. He drove me home from karaoke once, played with my hair, and it was magical. Next time he was in town, I invited him over. He thought we should have a "date" before we spent the night together, so we met with some people for wings, and then he came over. He never really left! We didn't have sex for the first few weeks, he even brought me home for Christmas before we took that step. We just felt this amazing connection right away, and there was no stopping that magical force.
For myself, I find that I either feel a romantic attraction / energy attraction, or I don't. I have never had romance develop from a friendship. Once you get put in my "just friends" box, there you shall always remain. I have, however, been able to become just friends with ex-lovers, after there has been some time apart to allow the feelings to dissipate.
That being said, I never go out looking for romance. It will come when it's meant to. I sometimes go out looking for friends, but I'm very introverted and I have 2 good friends in town and some friendly colleagues at school, so those needs are met.
Gralson = my husband
Auto = my girlfriend